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arXiv:1407.4997 · Physical Review A

Control of populations of two-level systems by a single resonant laser pulse

Nikolay V. Golubev, Alexander I. Kuleff

Published Sep 9, 2014• 41 citations
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Abstract

We present a simple approach allowing one to obtain analytical expressions for laser pulses that can drive a two-level system in an arbitrarily chosen way. The proposed scheme relates every desired population-evolution path to a single resonant laser pulse. It allows one to drive the system from any initial superposition of the two states to a final state having the desired distribution of the populations. We exemplify the scheme with a concrete example, where the system is driven from a nonstationary superposition of states to one of its eigenstates. We argue that the proposed approach may have interesting applications for designing pulses that can control ultrafast charge-migration processes in molecules. Although focused on laser-driven population control, the results obtained are general and could be applied for designing other types of control fields.

DOI
10.1103/physreva.90.035401

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Abstract We present an analytical electric field expression to simultaneously control the population and phase dynamics of two-level quantum systems. The presented electric field is obtained by a reverse engineering technique after the desired population and phase evolution pathways of the system have been specified. Upon application of this laser field, the system is driven from an arbitrary quantum state superposition to the desired population distribution; meanwhile the phase of one of the states proceeds according to a predefined path. The robustness of the engineered electric field is demonstrated by numerical simulations on the example of the 3s → 3p transition of atomic sodium. Furthermore, the limitations of the presented technique, which arise due to the application of the rotating wave approximation, are thoroughly analyzed and discussed.
In this paper, based on the idea of reverse engineering, we propose a scheme to find analytical expressions of a laser pulse that allows for controlling the evolution of two-level systems as desired, regardless of the time-dependent phase of the system. The pulse relates to particular functions that predefine the evolution of a system. For illustration, we present concrete examples of driving the system from an arbitrary initial state to a final state along the user-prescribed particular way in both closed and open quantum systems. Simulation results indicate that the desired evolutionary path is accurately obtained when the rotating wave approximation (RWA) is satisfied. Most importantly, the scheme allows us to maintain system coherence and populations even in the presence of certain dephasing and thermal noises. Thus it may naturally find applications in quantum computing and quantum memories.
In the previous paper on this topic it was shown how, for a pulse of arbitrary shape and duration, the drive frequency can be analytically optimized to maximize the amplitude of the population oscillations between the selected two levels in a general many level quantum system. It was shown how the standard Rabi theory can be extended beyond the simple two-level systems. Now, in order to achieve the quickest and as complete as possible population transfer between two pre-selected levels, driving pulse should be tailored so that it produces only a single half-oscillation of the population. In this paper, this second (and final) step towards the controlled population transfer using modified (i.e. many level system) Rabi oscillations is discussed. The results presented herein can be regarded as an extension of the standard πππ-pulse theory - also strictly valid only in the two level systems - to the coherently driven population oscillations in general many level systems.
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We propose a scheme for coherent control of population transfer and arbitrary superpositions of quantum states by a single-chirped laser pulse in a Λ-type excited-doublet four-level system. It is shown that selective, efficient, and robust population transfer from the initial state to the target states (excited or ground) can be achieved via chirped adiabatic passage when the pulse bandwidth is smaller than about 1/10 of the energy separations between the excited-doublet levels and between the ground states. Moreover, arbitrary coherent superpositions between the excited-doublet states, or between the higher ground state and either of the excited-doublet states, can be created by appropriately tuning the chirp rate and detuning the laser field. The proposed flexible method of coherent control of population transfer and arbitrary superpositions between the initially unpopulated states requires only a single pulse, and is robust against variations in the laser parameters, which has potential applications in quantum information processing.
State-selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules, or quantum dots is the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision metrology, and quantum computing. Rabi oscillations are one of the simplest, yet potentially quite useful mechanisms for achieving such manipulation. Rabi theory establishes that in the two-level systems resonant drive leads to the periodic and complete population oscillations between the two system levels. In this paper an analytic optimization algorithm for producing Rabi-like oscillations in the general discrete many-level quantum system is presented.